In 1998, Artés, Kooij and Llibre proved that there exist 44 structurally stabletopologically distinct phase portraits modulo limit cycles, and in 2018 Artés, Llibre andRezende showed the existence of at least 204 (at most 211) structurally unstable topologically distinct codimension-one phase portraits, modulo limit cycles. Artés, Oliveiraand Rezende (2020) started the study of the codimension-two systems by the set (AA),of all quadratic systems possessing either a triple saddle, or a triple node, or a cusppoint, or two saddle-nodes. They got 34 topologically distinct phase portraits modulo limit cycles. Here we consider the sets (AB) and (AC). The set (AB) contains allquadratic systems possessing a finite saddle-node and an infinite saddle-node obtainedby the coalescence of an infinite saddle with an infinite node. The set (AC) describes allquadratic systems possessing a finite saddle-node and an infinite saddle-node, obtainedby the coalescence of a finite saddle (respectively, finite node) with an infinite node (respectively, infinite saddle). We obtain all the potential topological phase portraits ofthese sets and we prove their realization. From the set (AB) we got 71 topologicallydistinct phase portraits modulo limit cycles and from the set (AC) we got 40 ones.
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